Income Taxes (Additional Information) (Details) - USD ($)	3 Months Ended
Mar. 31, 2023	Mar. 31, 2022
Income Tax Disclosure [Abstract]
Deferred tax assets, valuation allowance income tax expense (benefit)	$ 14,000	$ 0

Deferred tax assets valuation allowance income tax expense (benefit).

No definition available.

Name:	lyra_DeferredTaxAssetsValuationAllowanceIncomeTaxExpenseBenefit
Namespace Prefix:	lyra_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration